On dissipativity, passivity and dynamic operability of nonlinear processes

Passivity and dissipativity have long being important tools in nonlinear systems analysis and control design. In this article, connections between dissipativity and the dynamic operability of nonlinear processes are explored. In particular, we study nonlinear processes that are dissipative with respect to a supply rate quadratic in the inputs and outputs. These type of dissipative systems include processes that can be unstable and can have unstable zero dynamics. Two methods to quantify operability are proposed. The first method analyses the speed of response of the closed-loop with no exogenous signals. The second method studies the output disturbance attenuation problem. The proposed framework reveals important insights into those nonlinear process characteristics that can limit dynamic operability.     

ISE-optimal nonminimum-phase compensation for nonlinear processes

This work concerns the optimal regulation of single-input–single-output nonminimum-phase nonlinear processes. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton–Jacobi theory and the normal form representation of the nonlinear system. A Newton–Kantorovich iteration is developed for the solution of the pertinent Hamilton–Jacobi equations, which involves solving a Zubov equation at each step of the iteration. The method is applied to the problem of controlling a nonisothermal CSTR with Van de Vusse kinetics, which exhibits nonminimum-phase behaviour.     

Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control

We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that MPC with a nominal prediction model and persistent but bounded disturbances has some degree of inherent robustness when the terminal control law and the terminal penalty matrix are chosen as the linear quadratic control law and the related Lyapunov matrix, respectively. We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not depend on the continuity of the optimal cost function or of the control law in the interior of the feasible region.     

Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.     

Input–output decoupling of nonlinear systems by static measurement feedback

This paper gives necessary and sufficient conditions for solvability of the strong input–output decoupling problem by static measurement feedback for nonlinear control systems.     

Controller design for a class of nonlinear systems with input saturation using convex optimization

In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed.     

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

This paper considers certain practical aspects of the identification of nonlinear empirical models for chemical process dynamics. The primary focus is the identification of second-order Volterra models using input sequences that offer the following three advantages: (1) they are “plant friendly;” (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the first of these advantages, this paper defines a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra–Laguerre model. To illustrate the practical utility of the input sequences considered here, second-order Volterra and Volterra–Laguerre models are developed that approximate the dynamics of a first-principles model of methyl methacrylate polymerization.     

A novel modeling and controlling approach for high‐order nonlinear systems

This paper proposes a completely data–driven control law for a class of high–order nonlinear systems based on their virtual characteristic models. With sampled–data techniques and estimation methods, a novel lower–order adaptive characteristic model is constructed to reduce the system complexities. Moreover, a corresponding sliding mode control law is designed, which can guarantee tracking errors of the resulting closed‐loop system converging into a predefined bound in finite time. The practical examples are provided to illuminate the effectiveness of the proposed approaches.     

Least-squares LTI approximation of nonlinear systems and quasistationarity analysis

Least-squares linear time-invariant (LTI) approximation of discrete-time nonlinear systems is studied in a generalized harmonic analysis setting extending an earlier result based on quasistationary signals. The least-squares optimal LTI model is such that the crosscorrelation between the input and the LTI model output equals the crosscorrelation between the input and the output of the nonlinear system. New results for limits of sample averages of signals are derived via Riemann-Stieltjes integration theory. These results are applied to crosscorrelation and quasistationarity analysis of input-output signals for several important classes of nonlinear systems, including stable finite memory, Wiener and Hammerstein systems. This analysis demonstrates that the assumptions used in the least-squares LTI approximation setup are fairly mild. Finally, an illustrative example is provided.     

基于动态过程模拟的定量化HAZOP分析方法

HAZOP分析是一种广泛使用的过程安全评价方法,但缺乏定量化的评价依据。为了有效地辨识过程工业中潜在危险,在传统HAZOP方法基础上,提出了基于动态过程模拟的定量化HAZOP分析方法。首先进行HAZOP分析,辨识偏差原因和后果,然后建立动态过程模拟模型,通过预制故障模拟不同程度偏差原因对偏差后果的动态影响,得到偏差原因与后果之间的量化关系,并且通过模拟获得偏差原因的安全操作极限数据,分析现有安全保护措施的有效性,最后对偏差的调节措施进行模拟优化分析。为了验证所提出方法的有效性,以某气体分馏装置脱丙烷单元作为应用实例,采用Unisim软件建立动态过程模拟模型,对HAZOP偏差—“脱丙烷塔顶压力过高”的危险场景进行了模拟。研究结果表明,所提出的方法是对传统HAZOP分析的补充和扩展,实现了HAZOP偏差的定量化,从而提高了HAZOP分析的准确性和可靠性,对过程安全管理具有重要指导意义。     

Improvements of nonlinear dynamic modeling of hot-film MAF sensor

The operating procedure of engine requires that the mass air flow (MAF) sensor can measure the pulsation air flow accurately. Therefore the MAF sensor must possess fast response speed. It is necessary to study the dynamic characteristic of the MAF sensor. Both the experimental equipments and method used by authors previously are improved to obtain the sensor response data accurately in this paper. The static and dynamic separable modeling method is adopted to build the uniform nonlinear dynamic model of the hot-film MAF sensor in the Hammerstein and Wiener forms, which can describe the large/small flow-rate and positive/negative step responses. The performance indexes are calculated by the actual and model responses.     

A sequential LQG approach to nonlinear tracking problem

A new approach, named the sequential LQG solution for nonlinear and nonstationary systems tracking problem, has been proposed in the article. Proposed method for tracking of a desired reference trajectory uses a state space model of the multivariable nonlinear/nonstationary system. The method involves three steps. The first step is the design of nominal trajectory using the predictive control technique. The second step is the sequential linearization of the nonlinear system around the fixed operating points, chosen in accordance to the plant dynamics changes. The third step involves the choice of the weighting matrices in the classical LQG controller design for the sequence of linearized models. The feasibility of the proposed method has been demonstrated through its application to the control of aircraft, represented by the six-degree-of-freedom model around the prespecified nominal trajectory.     

Stabilization of nonlinear systems: A bilinear approach

This paper gives a necessary and sufficient condition for the stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.     

A new functional expansion for nonlinear systems

In this paper, we shall introduce a new functional series expansion of the output of a general nonlinear system as power series in powers of derivatives of the input components. We shall illustrate the usefulness of this series by considering two important problems namely those of “realization” and systems inversion.     

Analysis and control of parabolic PDE systems with input constraints

This paper develops a general framework for the analysis and control of parabolic partial differential equations (PDE) systems with input constraints. Initially, Galerkin's method is used for the derivation of ordinary differential equation (ODE) system that capture the dominant dynamics of the PDE system. This ODE systems are then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed-loop stability in the presence of constraints. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator. The theoretical results are used to stabilize an unstable steady-state of a diffusion-reaction process using constrained control action.     

A blind approach to the Hammerstein-Wiener model identification

In this paper, we propose a blind approach to the sampled Hammerstein-Wiener model identification. By using the blind approach, it is shown that all internal variables can be recovered solely based on the output measurements. Then, identification of linear and nonlinear parts can be carried out. No a priori structural knowledge about the input nonlinearity is assumed and no white noise assumption is imposed on the input.     

A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure‐feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite‐time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the ‘explosion of complexity’ problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed‐loop control performance is significantly improved when it is used in dynamic surface control instead of first‐order filters. The L _∞ stability of the whole closed‐loop system, which guarantees both the transient and steady‐state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign.This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.